Michael Gove has already committed one controversial act, with regard to children's health, by dismantling the network of school sports co-ordinators that had increased the amount of exercise undertaken by pupils – a simple and inexpensive response to the fear that sedentary lifestyles are breeding a generation of youthful couch potatoes. Despite widespread condemnation then, the education secretary seems determined to undo another successful, child-friendly policy bequeathed by Labour: healthy school food.

As we report today, some of the academies, beloved by Mr Gove, are not serving the nutritious fare that is now the norm in other state schools. They are also making money by selling sweets and crisps in vending machines, a practice Labour banned as part of its response to Jamie Oliver's 2005 television exposé of unhealthy school food. The minister has allowed academies and free schools to opt out of the requirement that canteen fare has to meet nutrient-based standards. So as the number of academies grows, the number of pupils certain to receive healthy dinners will decline. Oliver is among those who fear that Gove is undermining an innovative and beneficial system that should be maintained, not weakened. The minister also ended the School Lunch Grant as a dedicated pot of money for head teachers to improve their canteens. His stance puts at risk the better behaviour and improved concentration that well-balanced lunches have brought.

Gove is not the only senior member of the government whose judgment on how to tackle obesity needs to be questioned. Andrew Lansley, the health secretary, prefers to address the country's profound problems of bad diet via a voluntary "responsibility deal" with the food industry, rather than through legislation. It is a naive response, and one which the Academy of Medical Royal Colleges, the most influential medical body in the land, described last week as "inherently flawed" and doomed to fail.

Jamie Oliver, interviewed in today's Observer Food Monthly, laments the lack of government action on obesity. His judgment is a harsh one, but difficult to dispute, given the coalition's lack of effective action. Professor Terence Stephenson, the doctor leading the academy's new inquiry into obesity, has floated possible measures, including "fat taxes", limits on fast-food outlets near schools and an end to "irresponsible" marketing of unhealthy foodstuffs. He believes the history of public health, on issues such as seatbelts, drink-driving and smoking, shows that sometimes government action is needed, and that obesity's worsening effects – as a cause of illness, a drain on the NHS and a drag on people's self-esteem – make this another such moment.

David Cameron should take heed. He ignored his health secretary's opposition and sided with the medical establishment when he recently embraced minimum pricing of alcohol to reduce drink-related problems. On obesity he must be similarly bold.

No one doubts it is a huge cultural, political and behavioural challenge or pretends there is an easy solution. But if the answers, whatever they are, involve challenging corporate power and practices, legislating to improve the content of food or even limiting individuals' freedom to consume junk, then so be it. Only radical action will begin to win the challenge of obesity.